# Thread: Given that R is not reflexive, can R^2 be reflexive?

1. ## Given that R is not reflexive, can R^2 be reflexive?

Given that $\displaystyle R$ is a relation defined on a set $\displaystyle A$, and that $\displaystyle R$ is not reflexive, demonstrate whether it's possible for $\displaystyle R^2$ to be reflexive.

My first thought is that it's not possible, but I doubt that that's true...

2. What about the relation "is a brother of"?

3. Originally Posted by emakarov
What about the relation "is a brother of"?
Sorry, never heard of that one. I don't think it'd work anyways.

4. Originally Posted by Runty
Given that $\displaystyle R$ is a relation defined on a set $\displaystyle A$, and that $\displaystyle R$ is not reflexive, demonstrate whether it's possible for $\displaystyle R^2$ to be reflexive.
By $\displaystyle R^2$ I assume that you mean $\displaystyle R \circ R$.
If so, consider the set $\displaystyle \{a,b\}$ and the relation $\displaystyle R=\{(a,b),(b,b),(b,a)\}$.
Clearly $\displaystyle R$ is not reflexive. What about $\displaystyle R \circ R ?$